Radiative intensity is defined for any direction Ω, because the angular space is continuous. In order to handle the radiative intensity equation numerically, the angular space is discretized.
The discrete ordinates method provides a discretization of angular space. The quadrature sets Level Symmetric Even, Level Symmetric Hybrid and Equal Weight Odd are designed using moment-matching conditions (see Ref. 24) and yield S
N approximations with
N(N + 2) directions in 3D or
N(N + 2)/2 in 2D (see
Ref. 23). The quasi-uniform quadrature set yields T
N approximations with
8N2 directions in 3D or
4N2 in 2D (
Ref. 46,
Ref. 47). These approximations are not designed using moment-matching conditions but allow for higher-order discretization compared with S
N approximations.
Depending on the value of N, a set of
n dependent variables has to be defined and solved for
I1,
I2, …,
In.
In Equation 4-121, the first term in the right hand side is the emitted radiative intensity, while the second term represents the reflected radiative intensity.
In Equation 4-122, the right hand side is composed of the emitted radiative intensity, the reflected radiative intensity, and the radiative intensity transmitted in a diffuse and specular way.
The Incident Intensity (Radiation in Participating Media and Radiation in Absorbing-Scattering Media Interfaces) node defines a boundary that receives incident radiative intensity
Iext and that is transparent for outgoing intensity:
The node Radiative Source accounts for a directional power density
Ii in the radiative transfer equation:
, with
.